Quantitative electron-probe microanalysis of carbon in binary carbides

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Quantitative electron-probe microanalysis of carbon in binary

carbides

Citation for published version (APA):

Bastin, G. F., & Heijligers, H. J. M. (1984). Quantitative electron-probe microanalysis of carbon in binary carbides. In A. D. Romig, & J. I. Goldstein (Eds.), Microbeam Analysis : Proceedings of the 19th Annual Conference of the Microbeam Analysis Society, 16-20 July 1984 (pp. 291-294). San Francisco Press.

Document status and date: Published: 01/01/1984 Document Version:

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A. D. Romig Jr. and J. I.Goldstein, Eds., Microbeam Ana(l'sis-1984

Copyright@ 1984 by San Francisco Press, lnc., Box 6800, San Francisco, CA 94101-6800, USA

14 Computer-assisted Analysis

QUANTITATIVE ELECTRON·PROBE MICROANALYSIS OF CARBON IN BINARY CARBIDES

G. F. Bastin and H. J. M. Heijligers

Among the many problems connected with quantitative electron probe microanalysis of light elements (Z <10),1 there is one problem that, although recognized as early as 1975,2 has been grossly neglected since then and that is the fact that intensity measurements for these elements can no longer be performed at the maximum of the emission peak. Instead, intensi-ties have to be measured in an integral fashion--a direct consequence of the fact that in the K-ionization process of (for example) carbon the bonding electrons are involved, which leads, apart from shifts in the peak position that can be easily accounted for, to serious alterations

in

the shape of the C-Ka peak. leading in turn to an absolute necessity for integral measurements. If this factor is neglected errors of 30-50% are made, depending on the type of carbon standard. In the present case of binary carbides the problem can be overcome by the introduction of so-called Area/Peak (AlP) factors for each carbide, which represent the ratio between the (true) Area k-ratio and the Peak k-ratio. Once these have been established, future measurements can simply be carried out on the peak and multipli-cation by the appropriate AlP factor yields the correct k-ratio.

The next major problem is the choice of a correct ion procedure for matrix effects, of which absorption no doubt represents the major part. Unfortunately any correct ion procedure has to face the fact that the mass absorption coefficients for carbon are only known with little accuracy. An effort has therefore been made to produce a new set of consistent co-efficients using the "thin-film" approximation of Duncl,lmb and Melford. 3 Our own correct ion program,4 based on the use of modified Gaussian ~(pz) curves, was finally used to convert the measured k-ratios into concentrations, with excellent results: A relative root-mean-square value (calculated/true composition) of 3.7% over 117 k-ratios measured between 4 and 30 keV.

Experimental

For the measurements 14 binary carbides have been used (mostly of the groups IVA-VIA metals). the majority of which were prepared by arc-melting techniques in our own laboratory. With a few exceptions (line-compounds) the carbon content was determined independently by conventional combustion techniques.

Accurate Area/Peak factors with respect to Fe3C as a carbon standard were measured by stepping the spectrometer (JEOL 733 microprobe, take-off angle 40°) in small increments over the appropriate spectral range of the C-Ka peak and accumulating a large number of counts after each step. These counts were stored in the channels of a multichannel analyzer and displayed on the screen of a CRT. Finally the net (background subtracted) areas under the peak for both the unknown carbide and Fe3C were used to calculate the Area k-ratio. From the same spectra the Peak k-ratio was established. In this way a tot al of about 600 spectra were recorded. for some carbides over the full kV range; for others, mainly between 4 and

12 kV. All spectra were stored on floppy disk. As these measurements required long

dweIl-times (up to 3 h) on the same spot it was found imperative to use same kind of anticontami-nation device; an air jet turned out to be the only efficient option in the long run.

Finally, for improved statistics and to overcome the problem of slight inhomogeneities inevitably present in some carbides, a large number of peak k-ratio measurements were per-formed on 13 carbides at 9 different voltages between 4 and 30 kV. At each kV 50 measure-ments were carried out automatically on preselected areas of the specimen. This latter set

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of data, after multiplication by the appropriate

AlP

factors to yield the Area k-ratios, served as the database to which our correct ion program (BAS) was finally applied.

Results and Discussion

First it was established that the

AlP

factors for carbon were independent of voltage, contrary to earlier expectations,2 and that those for the metals were equal to 1. Figure 1 represents the results of the

AlP

measurements for carbon. The conspicuous sawtooth-like appearance, which is completely synchronous with the beginning and ending of a new period in the periodic system, is caused by the fact that carbides of notoriously strong carbide-forming metals like Ti, V, Zr, and Nb tend to yield relatively narrow and unambiguous emis-sion peaks, whereas carbides of elements like Si, Fe, Mo, and Wtend to develop shoulders in their profiles. As a consequence profiles of the former group have most of their inten-sity concentrated in a small region centered around the position of the maximum, with the result that peak intensity measurements would lead to a pronounced overestimation. The reverse applies to the latter group. It is quite obvious that errors of up to 30% are pos-sible if only peak measurements were carried out in the present case with Fe3C as a carbon standard. This error range would even deteriorate to 50% if glassy carbon with its broader peak had been used as a standard.

Figure 2 shows the results of the peak k-ratio measurements relative to Fe3C for TiC and ZrC which must be considered as two typical examples in the sense that in all carbides in which the absorption for C-Ka radiation is lower than in the Fe3C standard, the k-ratio v~ kV-curve exhibits a kind of saturation after an initial rise, followed by a downward bend (see upper curve in Fig. 2). The opposite is always found in systems with stronger absorption (lower curve). As mentioned, we have tried to use the "thin film" model,3 to test the existing sets of mass absorption coefficients on their internal consistency. If ever the conditions for this model to apply were satisfied, it would surely be in the present case for C-Ka radiation beyond 30 keV.

According to Duncumb and Melford, 3 the limiting k-ratio can be written as:

k

=

where ~(O) is the surface ionization (calculated according to Ref. 5), ~/p is the mass ab-sorption coefficient, and X is the weight fraction of carbon. The superscript refers to the type of radiation (C-Ka) and the subscript to the type of carbide. Two of the most recent sets of mass absorption coefficients for the examples in Fig. 2 are given in Table 1, to-gether with our own final values. The limiting peak k-ratios predicted by the thin film model using these various sets are indicated in Fig. 2 by dashed lines. It is evident that our set provides a better agreement between the predicted limiting k-ratio and the one ex-trapolated from the measurements up to 35-40 keV, than either of the other sets; and this conclusion is valid for all other carbides too.

Further support for the choice of the present mass absorption coefficients can be found in the results of the calculations of our correction program (BAS) in Fig. 3.

The fact that the calculated compositions are almost independent of voltage and the level merely shifts in a vertical direction according to the choice of absorption coeffi-cients could be taken as an indication that the ~(pz) curves predicted by our model are at

least fairly realistic. Anyhow, with the new set of coefficients a relative root-mean-square value (calculated/true composition) of 3.7% is obtained over 117 measurements, which shows that with proper care and procedures an accuracy can be obtained which is comparable to that of heavier elements. More details of this work will be supplied in separate publi-cations.

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•

@

I

WZC

•

B4C_i Fe 3C

I

•

I

• _wc

I TaC I

I

, ; I I

I • I

;

_i

,

I

!SiC I

I

• Cr3CZ I

_{I •}

!

•

HfC

I

• Cr7C3 _I t-bZC Cr23~ \

•

NbC VC

I

•

·Z:rC TiC

FIG. l.--Variation of areafpeak factors for C Ka radiation for various carbides relative to

Fe3C with atomie number of metal. 1.0 .9 .8 .7 5 14 22 24 26 40 4Z 7Z 74

- - - Atomie NlInber of metal

7

_ _ _ _ _ _ Aeeelerating Voltage (keV)

o

::;-0-~--1...0-~--2L-0-~--3 ....0-~---'40---l TiC .B ,-.. _AR u

....

oH

!

ZO §

...

.

~

••••

•

• ...

_m

• '"

8e~AA

...

_A _A 5 A A u ₁₅ 0 0 0 0 0 0

&

zrC AAA A A A A6 A 10

•

u"''''

...

•

0 0 0 0 0 0 0 0 5 0 10 ZO 30 40

• Aeeelerating Voltage (keV)

--- B ---- H ____ R

+~~

TiC(18.4 wt\ C) \ ZrC(8.55 wU C) \ . ----. H ' -...----._-••- - . - - - ----. B

•

---. R

I

4 5 3 ut"j &

a

.-4 6

e

FIG. 2.--Peak k-ratios for C Ka radiation relative to Fe3C for TiC and ZrC versus probe voltage. Dashed lines indicate

limiting k-ratio according to mass absorp-tion coefficients of Henke (H),6 Ruste (R),1 or present work (B). Bar~ indicate stand-ard deviation. For ZrC measurements

stand-FIG. 3.--Compositions calculated according to BAS program. Results for different sets of mass abs·orption coefficients indicated

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References

1. J. Ruste, "Principes généraux de la microanalyse quantitative appliquées aux éléments très légers," J. MicroBe. Electron. 4: 123-136, 1979.

2. W. Weisweiler, "Elektronenstrahl-Mikroanalyse von Kohlenstoff: V," Microchim. Acta

1975(11): 179-194, 1975.

3. P. Ouncumb and O. A. Melford, "Quantitative applications of ultrasoft x-ray micro-analysis in rnetallurgical problems," in R. Castaing et al., Eds., X-ray Opties and Micro-analysis3 Paris: Herrnann, 1966, 240-253.

4. G. F. Bastin, F. J. J. van Loo, and H. J. M. Heijligers, "Evaluation of the use of Gaussian ~(pz) curves in quantitative electron probe microanalysis: A new optirnization,"

X-ray Spec'3 1984, in press.

5. G. Love, M. G. Cox, and V. O. Scott, "The surface ionisation function ~(O) derived using a Monte-Carlo rnethod," J. Phys. 0-11: 23-31, 1978.

6. B. 1. Henke et al., "Low energy x-ray interact ion coefficients: Photoabsorpt ion, scattering, and reflection," Atomie Data and Nuclear Data Tables 27: 1-144, 1982.

TABLE l.--Most recent sets of rnass absorption coeeficients for carbon Ka radiation for the exarnples in Fig. 2.

Quantitative electron-probe microanalysis of carbon in binary carbides